An account is opened with an initial deposit of $7,500 and earns 3.6% interest compounded semi-annually for 30 years. how much more would the account have been worth if the interest were compounding weekly?

He would have had more $192.288 if the interest were compounding weekly

Step-by-step explanation:

Let us solve the problem in 2 steps

Step 1

We would determine the amount compounded semi-annually for 30 years.

Initial amount deposited into the account is $7,500. This means that the principal,P = $7,500

It was compounded semi-annually This means that it was compounded twice in a year. So

n = 2

The rate at which the principal was compounded is 3.6%. So

r = 3.6/100 = 0.036

It was compounded for a total of 30 years.

n = 30

The formula for compound interest is

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of n years.

A = 7500(1 + (0.036/2)^2×30

A = 7500(1 + 0.018)^60

A = 7500(1.018)^60

A= $21873.987

Step 2

We would determine the amount compounded weekly for 30 years.

Initial amount deposited into the account is $7,500. This means that the principal,P = $7,500

It was compounded weekly. This means that it was compounded 52 times in a year. So

n = 52

The rate at which the principal was compounded is 3.6%. So

r = 3.6/100 = 0.036

It was compounded for a total of 30 years.

n = 30

Applying the formula for compound interest,

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of n years.

A = 7500(1 + (0.036/52)^52×30

A = 7500(1 + 0.000692)^1560

A = 7500(1.000692)^1560

A = $22066.275

Difference in amount

= $22066.275 - $21873.987 = $192.288